Blow-up phenomena for linearly perturbed Yamabe problem on manifolds with umbilic boundary

TL;DR

This paper constructs blowing-up solutions for a linear perturbation of the Yamabe problem on manifolds with umbilic boundary, under specific geometric conditions including nonzero Weyl tensor and high dimension.

Contribution

It introduces a method to build blowing-up solutions for the perturbed Yamabe problem on manifolds with umbilic boundary, expanding understanding of geometric PDEs.

Findings

Blowing-up solutions are constructed under the given conditions.

Nonzero Weyl tensor is crucial for the construction.

Results apply to manifolds with dimension greater than 10.

Abstract

We build blowing-up solutions for linear perturbation of the Yamabe problem on manifolds with umbilic boundary, provided the Weyl tensor is nonzero everywhere on the boundary and the dimension of the manifold is n>10.